In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space associated with a kernel that reproduces every function in the space or, equivalently, where every evaluation functional is bounded. The reproducing kernel was first introduced in the 1907 work of Stanisław Zaremba concerning boundary value problems for harmonic and biharmonic functions. James Mercer simultaneously examined functions which satisfy the reproducing property in the theory of integral equations. These spaces have wide applications, including complex analysis, harmonic analysis, and quantum mechanics. Reproducing kernel Hilbert spaces are particularly important in the field of statistical learning theory because of the celebrated Representer theorem which states that every function in an RKHS can be written as a linear combination of the kernel function evaluated at the training points. More details can be found in [1]}, [2]}, [3]}.
